Crisis in the Foundation of Mathematics | Infinite Series

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•19 de out. de 2017
PBS Infinite Series
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Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What if the foundation that all of mathematics is built upon isn't as firm as we thought it was? Note: The natural numbers sometimes include zero and sometimes don't -- it depends on how you define it. Within logic, zero is always included as a natural number. Correction - The image shown at 8:15 is of Netwon's Principia and not Russell and Whitehead's Principia Mathematica as was intended. Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode How to generate Pseudorandom Numbers? | Infinite Series https://www.youtube.com/watch?v=C82Jy... Mathematics is cumulative -- it builds on itself. That’s part of why you take math courses in a fairly prescribed order. To learn about matrices - big blocks of numbers - and the procedure for multiplying matrices, you need to know about numbers. Matrices are defined in terms of - in other words, constructed from - more fundamental objects: numbers. References:: Probability website mentioned in comments: http://people.ischool.berkeley.edu/~n... https://plato.stanford.edu/entries/ph... https://plato.stanford.edu/entries/lo... Ernst Snapper :: https://www.maa.org/sites/default/fil... Philosophy of mathematics (Selected readings) edited by Paul Benacerraf and Hilary Putnam Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com) Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level! And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!
I feel very comfortable not having to write out a few hundred pages of justification whenever I need to add 1 and 1.
this is one of the best PBS's shows. They should hire her back!!
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My crisis in math is that I've covered vectors in 4 different classes now, and I still don't know any more about them than did after the 1st class.
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Frege: finally I can put a foundation to math Russell: think again bro Frege: woah you log-blocked me bro
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I'm 42 and this is the first time i encountered the dedekind cut. Ive lived fairly fine. But now that i know dedekind, watch out world... Here i come.
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The title scared me. I was expecting a Gödel's incompleteness theorem type discovery but more deadly.
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I swear when you said "What grounds mathematics?" I thought "It's turtles all the way down" and then you said it. I must be psychic
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This is still one of my favorite episodes, dealing with one of my favorite areas of math / philosophy. Infinite Series, as well as other channels like 3blue1brown, go a long way towards making complex math a lot simpler for peeps like me to follow. This / the world completely fascinates me :-)
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A video on foundations without mentioning Cantor, that’s something
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Admittedly I keep videos like this to help me fall asleep. Have to wake up early because I got a Cs and Ds in high school.
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Your pic of Russell's book is of Newton's Principia, which is 200 years older...
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Astronaut #1: Wait, it's all just turtles? Astronaut #2: Always has been.
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@9:00 I like how we just cruise past the implications of Gödel.
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The video I've been waiting to watch my entire life.
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No, please! Not another fascinating Youtube Channel! There isn't enough time to watch them all! ... oh well... SUBSCRIBED.
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I was REALLY hoping for Wittgenstein to show up after Russel, tearing down his work using their own "logicism methods". Mostly because he does it in such a badass way!
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This is like the problem of how do you define a word when its definition must contain another word and as such eventually you must do the nonsensical thing of using a word to define a piece of what defines it. Despite this we can communicate clearly and that just seems magical to me, and similarly maths seems solid and logical and clear despite it being based on axioms themselves with limited foundation. I think this type of thinking is just a wonderful part of the human condition as weird as it is to understand something you can't define without using itself.
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I was terrified when I first read about this years ago, and in a way I still am.
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I'm waiting to see if there will be a video without air quotes. (" ") She even did them in the comments section :D
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OMG! Your pronunciation of "Raphael" is perfect. Either you speak a romantic language fluently or your math skills make you linguistically smart.
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